Multiplying a vector by a positive real number
When a vector is multiplied by a positive number (for example 2, 3 ,5, 60 unit etc.) or a scalar only its magnitude is changed but its direction remains the same as that of the original vector.
Multiplying a vector by a negative real number
If a vector is multiplied by a negative number (for example -2, -3 ,-5, -60 unit etc.) or a scalar not only its magnitude is changed but its direction also reversed.
Triangle law of vector addition states that when two vectors are represented by two sides of a triangle in magnitude and direction taken in same order then third side of that triangle represents in magnitude and direction the resultant of the vectors.
Taken in same order mean tail of Vector B must coincide with head of vector A as shown in image.
If a vector is multiplied by a scalar as in , then the magnitude of the resulting vector is equal to the product of p and the magnitude of , and its direction is the same as if p is positive and opposite to if p is negative.
Distributive law for scalar multiplication:
A null vector is a vector having magnitude equal to zero.It is represented by .
A null vector has no direction or it may have any direction.
Generally a null vector is either equal to resultant of two equal vectors acting in opposite directions or multiple vectors in different directions.